Martinez is understood to have flown back from holiday to try and gain the services of Anderson for next season although he is not expecting to hear from the player until next week.
He has long since held the desire to complete the signing again of the player along with Manchester United striker Febian Brandy who spent the end of last season at the Liberty.
And his view is echoed by skipper Garry Monk who believes that both players would do a good job for the Swans next season after their spells here last season.
Speaking to the Evening Post, Monk said "It would be great if we could get Ando back, but that situation is out of the club's control
"The club can only do what it's done and give them a chance to prove themselves at a higher level.
"I know Forest are interested in Paul and his old man lives in Nottingham and is keen for him to go there.
"In football, things don't always work out and if he doesn't come, I'm sure someone else will.
"Febian is still really young. His talent's still quite raw and I don't think he knows how to play a striker's role fully yet.
"The Championship will be much better than League One, but if Febian comes back I'm sure he's good enough to adapt."
Earlier this week Huw Jenkins said that the club could not wait indefinitely for the two signatures but, certainly in the case of Anderson, it looks like Roberto is determined to get his man.